SOLUTION: A person's website specializes in the sale of rare or unusual vegetable seeds. He sells packets of sweet-pepper seeds for $2.48 each and packets of hot-pepper seeds for $4.88 each.

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Question 1198429: A person's website specializes in the sale of rare or unusual vegetable seeds. He sells packets of sweet-pepper seeds for $2.48 each and packets of hot-pepper seeds for $4.88 each. He also offers a 16-packet mixed pepper assortment combining packets of both types of seeds at $3.53 per packet How many packets of each type of seed are in the assortment?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
A person's website specializes in the sale of rare or unusual vegetable seeds.
He sells packets of sweet-pepper seeds for $2.48 each and packets of hot-pepper seeds for $4.88 each.
He also offers a 16-packet mixed pepper assortment combining packets of both types of seeds at $3.53 per packet
How many packets of each type of seed are in the assortment?
~~~~~~~~~~~~~~~ 

x packets at $2.48  and  16-x packets at #4.88.


Write the "money equation"

    2.48x + 4.88*(16-x) = 3.53*16  dollars


Simplify and find x

    2.48x + 4.88*16 - 4.88x = 3.53*16

         2.48x - 4.88x      = 3.53*16 - 4.88*16

               x            =  = 9.


ANSWER.  In the assortment, there are 9 packets at $2.48 and 16-9 = 7 packets at $4.88.

Solved.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The solution from the other tutor shows a standard algebraic solution method for 2-part "mixture" problems like this.

Here is an alternative which is often far less work, if the numbers in the problem are "nice".

Look at the three prices per packet -- $2.48, $3.53, and $4.88 (on a number line, if it helps) -- and observe/calculate that $3.53 is 105/240 = 7/16 of the way from $2.48 to $4.88.

That means 7/16 of the packets in the mixed assortment are the higher-priced hot pepper seeds.

Then, since the mixed assortment contain 16 packets of seeds, it contains 7 packets of the hot pepper seeds and 9 packets of the sweet pepper seeds.

ANSWER: 7 hot pepper packets, 9 sweet pepper
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